Comparison of Recent Acceleration Techniques for the EM Algorithm in One- and Two-Parameter Logistic IRT Models

Abstract

The expectation–maximization (EM) algorithm is an important numerical method for maximum likelihood estimation in incomplete data problems. However, convergence of the EM algorithm can be slow, and for this reason, many EM acceleration techniques have been proposed. After a review of acceleration techniques in a unified notation with illustrations, three recently proposed EM acceleration techniques are compared in detail: quasi-Newton methods (QN), “squared” iterative methods (SQUAREM), and parabolic EM (PEM). These acceleration techniques are applied to marginal maximum likelihood estimation with the EM algorithm in one- and two-parameter logistic item response theory (IRT) models for binary data, and their performance is compared. QN and SQUAREM methods accelerate convergence of the EM algorithm for the two-parameter logistic model significantly in high-dimensional data problems. Compared to the standard EM, all three methods reduce the number of iterations, but increase the number of total marginal log-likelihood evaluations per iteration. Efficient approximations of the marginal log-likelihood are hence an important part of implementation.